Aḥsab n tazgant inégrit (yettwassen daɣ d aḥsab n arcus tangent) iḥesab arctangent (atan) n yal timmad tamaddast tufa-t-id uzaɣar i tella tazgant-is d timmad-nni. Ma tettafaɣeḍ uzaɣar n uslal s usefru n tiẓri d tamsurt am ɣersiwen anneɛrur d amsurif, neɣ s tasneflit n tafenka n tazgant ɣer tifesnayin neɣ rradyanen, akardam-agi n uzaɣar ad ak-yefk adday dɣa. Ansa timeɣri tazziyt neɣ tafenka n ɣersiwen anneɛrur/amsurif seg uɣanib anneɛrur, fren gar tifesnayin d rradyanen, tufiḍ iddayen dɣa. Aḥsab arc tan-agi yessawer daɣ aɣraf n uɣanib idirghníomhach, yessutur aɣraf n arctan(x), yessken daɣ taffa n tazgant taččint—akk ayen یلا حاجة إليه للحسابات المثلثية والتفاضلية والملاحية في مكان واحد.
Tazgant Inégrit Aḥsab
Adday
Ittwḥesba arctan(1)
45°
Tifesnayin 45°
Rradyanen 0.7854 rad
Gradianen 50 grad
Aḥriq π π/4
Aɣanib Anneɛrur Idirghníomhach
Mɣer yal aḥsab, aɣanib itettbeggaɣ i wakken ad twaliḍ belli θ = arctan(anneɛrur / amsurif).
Aɣraf n tazgant inégrit
Aɣraf yessender imunas n wudem i wakken ad tqaranḍ timmad d uzaɣar-is.
D acu tazgant inégrit?
Tazgant inégrit, tettwarun d tan⁻¹(x), arctan(x), neɣ atan(x), tettar uzaɣar i tella tazgant-is d x. Deg imagrad n Turuft d Lalman, tfeksit-agi tella s arcus tangens neɣ arkus tangens.
Deg uɣanib anneɛrur, tan(θ) = anneɛrur / amsurif, s uyagi arctan(anneɛrur / amsurif) yefk uzaɣar θ.
Tamda-s d akk timmadin timaddasin, seg-nni tamawalt-is tazgggant d (-π/2, π/2) neɣ (-90°, 90°).
Idirghníomhach: Tamda d Tamawalt n arctan(x)
Beddel asliduy i wakken ad twaliḍ amek tessemmaɣ yal timunas tamaddast ɣer uzaɣar gar -90° d 90°.
Amek ara tettwḥesbu tazgant inégrit?
Sqedec θ = arctan(x) ma yella x d timeɣri tazziyt neɣ d tafenka.
- Af timeɣri x.
- Sqedec aḥsab n tussna neɣ ufeksil atan() i uḥsab n arctan(x).
- Senfeɣ adday ma tebɣiḍ tifesnayin deg umkan rradyanen. Tes adday n rradyan s 180/π i wakken ad tawḍeḍ tifesnayin.
Idirghníomhach: Aḥsab Azgen s Azgen
Aru timeɣri i wakken ad itbeddel yal azgen dɣa.
1Ionchur: x = 1
2arctan(1) = 0.7854 rad
3Senfeɣ: 0.7854 × 180/π = 45°
Amek ara tesqedceḍ aḥsab-agi n tazgant inégrit?
Fren ionchur tazziyt neɣ anneɛrur/amsurif, fren tifesnayin neɣ rradyanen, sit Eḥseb.
Isental n Iosiyen
1
Timeɣri tazziyt
Amur tazziyt yetteqbel timmadin am 0.5, 1, neɣ -2.75.
2
Anneɛrur / Amsurif
Amur Anneɛrur / Amsurif iqesem sin ɣersiwen seld syin isqedec arctan.
Tasna n waddayen tessken kra n tnaɣnin n tirrit i useqdec asasa.
Amek ara sqedceɣ tazgant inégrit deg uḥsab?
Sit taqeffalt '2nd' neɣ 'Shift' deg uḥsab n tussna (am Casio neɣ TI-84), syin sit taqeffalt 'tan' i wakken ad taweḍ ɣer tan⁻¹.
- Snulfu aḥsab uget amur n uzaɣar ɣer tifesnayin (DEG) neɣ rradyanen (RAD).
- Sit '2nd' neɣ 'Shift.' Taqeffalt-agi tesskelɛa ufeksilen wuddren uqbel yal taqeffalt.
- Sit taqeffalt 'tan'. Aɣraf ad d-yafint 'tan⁻¹(' neɣ 'atan('.
- Aru timeɣri syin sit '='.
Agziɣ Amɣarur: Naf tan⁻¹ deg uḥsab
Tugna d afella tessken tiqeffalin tucriḍin i wakken ad tsiteḍ deg uḥsab TI-84.
Naf tan⁻¹(1) = 45° deg uḥsab TI-84
Amek ara tettwḥesbu tazgant inégrit s ufus?
Sqedec taɣlelt n uzrar Taylor n arctangent i wakken ad tqerriḍ arctan(x) s ufus: arctan(x) = x − x³/3 + x⁵/5 − x⁷/7 + … Uzrar-agi ittawi yid-s ma yella |x| ≤ 1.
- Uzrar n Taylor (uzrar n Maclaurin). Akaram n tqerriḍt n arctangent isqedec x − x³/3 + x⁵/5 − x⁷/7. Ugar n tirmit tettawi ugar n tifrat.
- Timmadin n Uzaɣar Ittwaɛren. Ɛqel tiramrawin igesranen: arctan(0) = 0°, arctan(1) = 45°, arctan(√3) = 60°.
- Alguritem CORDIC. Tiɣawsa-agi deg umeskar iḥesab arctangent s taẓridwin n uzaɣar imsisreq.
Idirghníomhach: Tqerriḍt n Uzrar Taylor
Fren acḥal n tirmit i wakken ad tessineḍ. Ẓer amek tqerriḍt taweḍ ɣer timmad tacriḍt.
Aɣraf n tazgant inégrit
Aɣraf n arctan(x) d agef imataren s uẓar n S i yeddan seg tazwara isemmaɣ ɣer ±π/2.
- Yesɛa ifirasen cothrománacha deg y = -π/2 d y = π/2.
- D amẓur, s uyagi arctan(-x) = -arctan(x).
- Ittar dima seg azadur ɣer tama tayeffust.
Idirghníomhach: Aɣraf n arctan(x)
Ewet s yeɣef aɣraf i wakken ad tsbeddeḍ timmadin tucriḍin.
Taffa n tazgant
Sit yal tagdazalt n taffa i wakken ad tessirneḍ timmad-nni taɣelsant deg uḥsab.
| x | arctan(x) Tifesnayin | arctan(x) Rradyanen | Aḥriq π |
|---|---|---|---|
| −∞ | −90° | −1.5708 rad | −π/2 |
| −√3 ≈ −1.7321 | −60° | −1.0472 rad | −π/3 |
| −1 | −45° | −0.7854 rad | −π/4 |
| −1/√3 ≈ −0.5774 | −30° | −0.5236 rad | −π/6 |
| 0 | 0° | 0 rad | 0 |
| 1/√3 ≈ 0.5774 | 30° | 0.5236 rad | π/6 |
| 1 | 45° | 0.7854 rad | π/4 |
| √3 ≈ 1.7321 | 60° | 1.0472 rad | π/3 |
| +∞ | 90° | 1.5708 rad | π/2 |
Tirawalt n Inégrit n Tazgant
Tirawalt n inégrit n tazgant tesɛa 3 n tnaɣnin taɣelsanin: tan⁻¹(x), arctan(x), d atan(x).
- tan⁻¹(x) Aɣelsani deg iḥsaben ifizikanen.
- arctan(x) Taɣelsant deg tmaɣit taɣelsant.
- atan(x) Tirawalt n usenfar d isenfaren.
Kra n iɛelliyen semmant-as anti tangent acku ittmestay ayen yegga tazgant, tura mačči d tirawalt tamatematikt taɣelsant.
Idirghníomhach: Tqaranit n Tirawalt
Sit ɣef yal tirawalt i wakken ad tessneḍ anida tban deg tmaɣit, usenfar, d iḥsaben.
tan⁻¹(x) d tirawalt aɣelsant ugar deg iḥsaben ifizikanen. Ifris -1 d 'ufeksil inégrit,' mačči '1 / tan(x)'.
Naf tan⁻¹ n Timmadin Tilmidin
tan⁻¹ n timmadin tilmidin yettarra uzaɣar almid. Acku arctangent d ufeksil amẓur, arctan(-x) = -arctan(x).
- arctan(-1) = -45° neɣ -π/4 rradyanen
- arctan(-√3) = -60° neɣ -π/3 rradyanen
D acu tan⁻¹ n -1?
tan⁻¹ n -1 d -45° (-π/4 rradyanen neɣ -0.7854 rradyanen).
Idirghníomhach: Ambaɛɛan n Timmadin Tilmidin
Ansa yal timmad almid i wakken ad twaliḍ amek arctan isemmaɣ iosieyn ilmidin ɣer uzaɣaren ilmidin.
arctan(-1) = -45° = -π/4 rad
arctan(1) = 45° ↔ arctan(-1) = -45°
Isteqsiyen
Tirriyin n isteqsiyen igesranen fell-as n tazgant inégrit.
Ih, tan⁻¹ d tirawalt tamatematikt taɣelsant i tazgant inégrit, tettusemma daɣ arctangent neɣ arctan. Ifris ⁻¹ ur d-yesemmi ara 1/tan (armi d cotangent). Deg umkan-nni, tan⁻¹(x) yettsuter: 'Anwa uzaɣar i tella tazgant-is tettawi x?' Amedya, tan⁻¹(1) = 45° acku tan(45°) = 1.
Tfefres tfeksit tazgant uzaɣar-nni tufa-t-id deg tafenka n waddad azelmaḍ ɣer waddad amsurif deg uɣanib anneɛrur. Tazgant inégrit (arctan) tettegg ifrat: tettu tafenka tufa uzaɣar imkatten. Amedya, tan(45°) = 1, s uyagi arctan(1) = 45°.
Taqeffalt n tazgant inégrit tettili sdat n taqeffalt tan deg kra n iḥsaben n tussna. I wakken ad tt-tawḍeḍ, sit taqeffalt 2nd neɣ Shift syin sit taqeffalt tan. Aɣraf ad d-yafint tan⁻¹ neɣ arctan. Deg iḥsaben grafiken am TI-84, sit 2nd syin TAN.
Sqedec taɣlelt n uzrar Taylor: arctan(x) = x − x³/3 + x⁵/5 − x⁷/7 + ... i |x| ≤ 1. I timmadin n wudem, ɛqel timmadin n uzaɣar: arctan(0) = 0°, arctan(1/√3) = 30°, arctan(1) = 45°, arctan(√3) = 60°.
Tazgant inégrit n 1 d 45° (neɣ π/4 rradyanen). Ayagi acku tan(45°) = 1. Deg uɣanib anneɛrur anda ɣersiwen anneɛrur d amsurif d imkutten, uzaɣar d 45°.
Tan isenneɣ uzaɣar ɣer tafenka (anneɛrur/amsurif), maca tan inégrit (arctan) isenneɣ tafenka ɣer uzaɣar. Tan d timucuha teqqen-d yal timmad tamaddast, maca arctan yettarra uzaɣar yiwen d ameɣtu deg (-90°, 90°).
Ih, sqedec tanfalt =ATAN(value) deg Excel. Agi yettarra adday deg rradyanen. I tasneflit ɣer tifesnayin, sqedec =DEGREES(ATAN(value)). Excel yessiḍen daɣ =ATAN2(x, y) i arctangent s snat n tirzeɣ.
Snegded iPhone-ik ɣer uswir n tɣersiwin i wakken ad d-taffeɣ aḥsab n tussna. Sit taqeffalt 2nd i wakken ad tsbeddleḍ ɣer tfeksalin tinégriyin. Taqeffalt tan ad tsbeddel ɣer tan⁻¹. Ansa timeɣri-k syin sit tan⁻¹.
Deg uɣanib anneɛrur, tazgant inégrit n tafenka anneɛrur/amsurif tettawi uzaɣar deg uwṭṭun-nni. Ma yella anneɛrur = 3 d amsurif = 4, s uyagi arctan(3/4) ≈ 36.87°.
Llan 6 n isqedacen igesranen: (1) Aferru d GPS i uzaɣar n ubrid, (2) Tazedɣut i uzaɣar n uslal, (3) Fizik i ivekturen n tẓallit, (4) Tseɣnit n uqemmam i tduri, (5) Tazedɣut tulanit i uzaɣar n umḍiq d wulawen, (6) Timzizit i uzaɣar n taẓa.
S tan(θ) = sin(θ)/cos(θ). Ma yella θ = arctan(x), s uyagi sin(θ) = x/√(1+x²) d cos(θ) = 1/√(1+x²). Tifaskit n arctan(x) d 1/(1+x²).
Ih. Tafenka n uslal d tamwant am anneɛrur uqbel amsurif deg uɣanib anneɛrur. Ansa tirzit-ik am waddad anneɛrur d taẓeggit-ik am waddad amsurif akk d akardam ad d-yettarra uzaɣar n ustiy deg tifesnayin d rradyanen.
Akardam-agi yettwasnikeɛ s uṣeṭṭa i arctangent. Ma tebɣiḍ aḥsab inégrit n uɣanib d ameqqran yessiḍen arcsin d arccos akk d arctan, ttarakeḍ akardam w uɣanib inégrit d ameqqran.